Housing equity withdrawal for development of assisted-living facilities

1.1 The motivation for this article

In the European Union (EU), currently, 40 million older people depend on the help of others. This number will increase to 55 million in 40 years. More than 4 million dependent older adults live in segregated residential institutions that are not able to guarantee person-centred services to achieve the total inclusion of the elderly in the community. According to The Ageing Report 2015 (European Commission, 2015a, 2015b), the number of dependent older adults will double by 2060. Human dignity and respect for human rights guide European Member States to implement the deinstitutionalisation of long-term care (LTC) systems. According to Principle 18 of the European Pillar of Social Rights on LTC “everyone has the right to affordable LTC services of good quality, in particular home-care and community-based services. Following also the provisions of the Convention on the Rights of Persons with Disabilities (United Nations, 2006) and the European Convention on Human Rights (Council of Europe, 1950), European member states must implement measures that strengthen the transition from an institutional to community-based facilities and services. As stated by the Innovation Union [European innovation partnership on Active and Healthy Ageing (EIP on AHA), 2015]:

[. . .] the building stock in Europe today is not fit to support a shift from institutional care to the home-based independent living model. Some 70-80 per cent of houses in the UK and 90 per cent in Germany are not suitable for independent living as they contain accessibility barriers for people with emerging functional impairments and chronic conditions.

This deinstitutionalisation procedure requires building new facilities for the elderly and remodelling their homes to adapt them to people with declining functional capacities and to organise a new logistic network in an accurately determined functional region (Drobne and Bogataj, 2014, 2015, 2016; Szander et al., 2017). We need to develop a sufficient number of the following care facilities:

• Independent living communities;

• Assisted-living facilities;

• Residential care facilities;

• Continuing care communities; and

• Nursing Homes (NHs), to provide the assistance and care of people who depend on the help of others and whose functional abilities are decreasing.

For different levels of functional capacity of the elderly, various facilities are needed. The burden of investment lies mainly with local communities, but the taxes and other social assets are not sufficient to meet the needs of the elderly (Janež et al., 2016).

Life expectancy in Europe is increasing but expected healthy years are not following an increase in life expectancy. How to provide quality services and housing for an increasing number of people that are dependent on the help of others is a crucial question in the EU. By the »operational programme for the implementation of the European Cohesion Policy for the period 2014–2020«, as a critical area, Slovenia identified promoting the availability of affordable, sustainable and high-quality services, including health and social services of general interest also for old inhabitants. These services include LTC. Slovenian National housing programme 2015–2025, prepared by the Ministry of the environment and spatial planning envisioned the development of assisted-living facilities with 10,000 housing units. The programme also states that there are currently no financial resources allocated for the development of these facilities. In the paper, we present a model for financing the construction of assisted-living housing units with a current equity of senior homeowners, which are dependent on the help of others. The critical issue is how to develop a quantitative model for measuring and forecasting a long-term demand for LTC services and facilities for the elderly and how to plan and finance the assisted-living facilities for seniors with declining functional capacities, which will be available by the demand.

1.2 Reverse mortgage in the Web of Science literature

The reverse mortgage is a type of home loan that allows a borrower to open a line of credit while using his home as collateral. With the loan model, the beneficiary draws liquid amounts in lump-sum or/and periodically from the value of the real estate (VRE) in the form of a loan secured by a mortgage on the real estate. With the part of this liquid amount that is drawn from the real estate, the beneficiary purchases deferred lifetime annuity in the form of a monthly (or yearly) premium (PR).

The novelty in this paper is the inclusion of LTC insurance that covers expenditure for care when a person becomes dependent on the help of others. In this way, the beneficiary insures his longevity so that if he lives longer than his life expectancy and LTC expenditures that is contingent on the category of needed care when he becomes dependent on the help of others, he will receive a lifetime annuity until his death. In the paper, we propose the reverse mortgage model with the insurance for longevity, where the periodic disbursement that the beneficiary receives is the difference between the amount drawn and the annuity PR for longevity insurance. In this way, if the beneficiary survives the drawing period of a reverse mortgage (n years), he receives a lifetime annuity that covers the disbursement to the recipient and the interest on the outstanding loan. This is a new scheme, first proposed in Bogataj (2013a, 2013b) and now developed further. Generally, loan models allow the beneficiary to draw the VRE in different ways:

• In lump sum – at the closing of the reverse mortgage contract;

• In the form of a line of credit so that he can draw it when necessary; and

• In uniform periodic amounts in the period of life expectancy.

The model could belong to the set of models considering equilibrium in competitive insurance markets In case of imperfect information (Rothschild and Stiglitz, 1976), but the list of articles in Web of Science (WoS) dealing with the topic “asset-based policies” goes back only to 1995 and their number grows very slowly as given in Table 1, while the list of articles also dealing with “home-ownership” is shorter; there are only 30 papers in WoS. Rasmussen et al. (1997, electronic version 2010) were considering the reverse mortgage as an asset management tool at the end of the past century. Unlocking housing equity through reverse mortgages was developed in Australia already in the first decade of this century (Ong, 2008; Davis, 2009). First, four papers on homeownership in WoS were published in 2009 and there is no growth of intensity. However, among articles dealing with “asset-based policies” and “equity release” we found only eight items in WoS while there are only two papers in the WoS Core Collection dealing with “asset-based policies” and “reverse mortgage (Bogataj, 2013a, 2013b; Haffner et al., 2015). Haffner et al. investigated whether there are links between institutional context and the development of markets in home equity conversion that are based on financial instruments facilitating mortgage equity withdrawal. Based on the secondary data and literature review considering four older EU member states, USA and Canada. They exposed that there are, in principle, three channels of housing equity withdrawal in the developed countries, namely:

1. mortgage equity withdrawal;

2. trading on where owners move from one dwelling to another but hold a lower amount of housing equity in the home they purchase; and

3. selling up.

As their countries in the investigation had similar per capita GDPs, therefore, at the same stage of economic development, from their paper, it is not clear what are possibilities in less developed countries. They also refer to Doling and Ronald (2010b) on “property-based welfare and European homeowners: How would housing perform as a pension”, where a significant positive correlation between before-housing poverty rates among over 65 s and the rates of homeownership in a sample of EU countries has been proved. Haffner et al. also exposed tax rules, which can also deter or incentivise mortgage equity withdrawal. They have not even overlooked the fact of exposure to the risk of various mortgage equity withdrawal programmes such as in the USA, where now the Home Equity Conversion Mortgage insurance, provided by Housing and Urban Department of US Government, ensures that reverse mortgages that are offered to homeowners 55+ years old are affordable and the reverse mortgage legislation stipulates that the products are safe and reliable for users.

However, Haffner and al. concluded that “it is conceivable that unmeasured cultural or other differences exist that might also be responsible for the evolution of mortgage equity withdrawal in each country”. In the welfare systems of Souther European countries have traditionally been met more by the family, according to our investigation, especially in rural areas, the elderly are primarily taken care of by families (Bogataj et al., 2016). Practices of intergenerational support for homeownership among different generations of families are also described in Manzo et al. (2019), where they stressed the role of homes and housing assets in mediating dependence and re-affirming family ties and relationships.

The welfare systems of Eastern European Countries have usually been achieved by state social protection measures and by the family, while the ownership structure has been dramatically changed after the transition in the nineties, after the privatisation of public housing and reduction of public social housing (Bogataj, 2013a, 2013b; Mandič, 2010). After the intensive research of East Asian cases, Doling and Ronald (2012) wrote that:

[. . .] in the welfare systems of East Asian countries, the income, care and other needs of older people have traditionally been met less by state social protection measures and more by the family, supported by what might be termed the first homeownership strategy: widening access to home ownership as a physical, emotional and financial basis of family wellbeing.

Equity release schemes (ERS) fall under the list of instruments that support the asset-based welfare of the older adults for their assets rather than their pensions. Asset-based welfare bases on the stock of capital that one holds and not just his yearly income.

Asset-based welfare is based on the statements that an economy can achieve a path towards prosperity if the individuals accumulate and acquire assets. According to Paxton’s theory, the stock of capital is the real measure of well-being. The asset-based approach to welfare provision is a theoretical model based on the theoretical assumption that housing is a good that enables the flow of other household goods and services and the “pillar under the welfare state” (Torgersen, 1987; Malpass, 2008) or “cornerstone of welfare” (Doling and Roland, 2010a, 2010b; Ronald and Doling, 2012). The theory is spreading from the UK to some other countries and is leading to a more market-oriented housing policy (Ronald and Doling, 2012). Risk individualisation through asset creation is also prevalent in post-socialist transition countries, as evidenced by the high levels of homeownership, as the ratio of owner-occupied units to total residential units in a specified area, after the privatisation of public housing and the dramatic reduction of public social housing (Mandič, 2010).

The details in 2013 and 2014 are given in Table 2. Homeownership rates have declined after the financial crisis in many countries, particularly in South-Europe, but in Eastern European countries not so much. There most of the properties are mortgage-free because of the national privatisation programmes in the nineties.

1.3 The structure of this article

As housing is an essential component of welfare strategies for homeowners (Soaita et al., 2017), for the ageing societies, which are subject of our investigation, we join the advice that housing wealth would be an excellent asset to be withdrawn to compensate for reduced income after retirement (De Decker and Dewilde, 2010; Malpass, 2008, Bogataj and Bogataj, 2015, Bogataj et al., 2016) and essential for the LTC provision. Thus, the objective of the paper is to present how to develop an actuarial model for determining the capacities for LTC in different types of facilities in the system. Therefore, after discussing the right to suitable accommodation as the human right in Paragraph 2 and the presentation of specialised housing for older adults in Paragraph 3, in Paragraph 4 the data collection is discussed. The article also presents the proposal for a model of collecting and processing data in the system of statistical reports relevant for the whole country, to better forecast the long-term needs of facilities for seniors with declining functional capacities. In Paragraph 5, we have extended the existing loan reverse mortgage model presented in Bogataj (2013a, 2013b) and Bogataj and Bogataj, 2015. The challenge is EU-wide, but the numerical example is given for Slovenia. The probabilities are derived from the data provided by the Slovenian institutions. The general formula can be useful for any EU member state. In all EU Member States, the LTC is provided according to the categories of care but the number of categories is varying from 3 to 7. Actuarial methods based on the equivalence of the actuarial present values and the multiple decrement approach we further developed to evaluate PRs for flexible longevity and lifetime LTC insurance for financing adequate facilities. Our studies show that currently available reverse mortgage contracts lapse when the homeowner moves to assisted-living facilities in any EU Member State, while in our article a new method is developed where multiple adjustments of housing to the functional capacities with relocation is possible under the same insurance and reverse mortgage contract. For a numerical example, we have calculated the case of Slovenian reverse mortgage programme in Paragraph 5.4. After the discussion in Paragraph 6, we suggested conclusions and directions to further research.

4.1 Measuring the care dependency in European Union

Statistical monitoring of the number of beneficiaries and the financing of LTC is a crucial base for the efficient and effective planning of spatial capacities and necessary human resources for carrying out LTC activities. The data are scattered across many institutions and sources. Preferences of Europeans for LTC provision are presented by Eurobarometer 283 (EC, 2007). Population projections for the European population for period 2018–2020 were made by EUROSTAT (Eurostat, 2018) and Budgetary projections for the period 2016–2070 are published in The Ageing report 2018 (EC, 2018a). Systematic reviews of organisations of LTC provision and LTC funding by some European and other countries are presented in the study of European Commission “challenges in LTC in Europe: A study of national policies” (Spasova, et al., 2018). In Europe, the issue of LTC has already been addressed by the European Commission (2010) and later by Ujvari (2012) and Bocquaire (2016).

In EU Member states the public LTC provision could be wholly or partly financed through health insurance schemes, LTC insurance schemes and state budgets). Eligibility for partially publicly funded LTC services can be subject to care needs of the dependent person, his or her income and assets and the availability of family carers. For assess the care needs, a home visit is usually carried out by the social services but the statistics on needs are not available for planning purposes. The assessment of care needs is increasingly based on a functional assessment, using a scale defining the degree of care dependency.

The system of LTC provision in England has 4 categories of care where care needs are defined as (I. – critical, II. – crucial, III. – moderate and IV. – Low) and presented by Comas-Herrera et al. (2010). LTC system in Hungary has 8 categories of care as presented by Czibere and Gal (2010). Bulgaria has 3 categories of LTC (I. > 90% dependent, II. In total, 71%–90% dependent, III. In total, 50%–70% (Riedel and Kraus, 2010). LTC system in Austria has 5 categories of care according to the number of hours of care needed (I > 60 h, II > 85h, III > 120 h, VI >160 h, Va, b, c >180 h per month). In Germany, the scale of dependency consists of four categories of LTC insurance I, II, III, III+, which depends on the number of hours of assistance and care needed, as described by Arntz et al. (2007) and Schulz (2010a, 2010b). System of LTC provision in Slovenia has 4 categories from the lowest needs (I) to the highest needs (IV) as presented by Rupel-Prevolnik and Ogorevc (2010) and Kavšek and Bogataj (2017). Category of care I–III can also be provided as homecare or in assisted living housing, but the LTC of category IV can only be provided in a NH.

One of the best-structured systems of LTC provisions is organised in Spain where they have 3 categories of care, each divided into two levels according to the need of user and number of hours of care as presented in Gutiérrez et al. (2010). Therefore, after examining the organisation of LTC across the EU Member States, we selected the Kingdom of Spain as a useful example of how to regulate the system of LTC provision and how to institute comprehensive information system for recording LTC users and services.

The care of the elderly is legally defined under the auspices of the Ministry of Health, Social Services and Equal Opportunities (Spanish Ministerio de Sanidad, Consumo y Bienestar Social, Servicios Sociales e Igualdad) under the following laws:

• The Act on the Promotion of Independence and Care of Persons Dependent on the Assistance of Others (Boletin Oficial del Estad, 2006);

• Act on the Rights of Persons with Reduced Functional Abilities and Their Social Inclusion (Boletin Oficial del Estad, 2013a);

• Royal Decree 174/2011, which sets the scale for assessing the ability of self-sufficiency or addiction (Boletin Oficial del Estad, 2011);

• Royal Decree 1050/2013, which places a range for evaluating the ability of autonomy or dependence (Boletin Oficial del Estad, 2013b); and

• Decision SSI/2371/2013, which regulates the information system for monitoring dependency on 18 December 2013 (Boletin Oficial del Estad, 2013a, 2013b).

The Act on the Promotion of Independence and Care for Persons Dependent on the Help of Others (2006) regulates the system of LTC. It provides a catalogue of essential services and benefits to which all citizens are entitled. The Act determines, which services are directly accessible in the community and for which the beneficiary receives cash benefits, sets the criteria for determining the amount of remuneration, the level of participation of the recipients in the cost of services and sets the scale for the assessment of functional capabilities. The law provides a system of assistance to achieve the maximum possible autonomy and care of people who are dependent on the help of others. (Bogataj et al., 2015). However, there is no unified information system to be able to measure the quality of services.

4.2 Long-term care information system

For the development of LTC insurance product embedded in reverse mortgage housing equity withdrawal, statistical data on LTC provision and needs and housing needs are of significant importance. LTC information system should record the following data of applicants and beneficiaries (Table 3):

For better support of spatial planning and timely investments in facilities for older inhabitants, also the detailed description of the current housing of seniors should be included in an information system. Such details would allow for better planning and development of proper assisted-living facilities.

The range of social services for care-dependent older people can vary widely between and within countries in terms of the care provided. Social care includes home care, semi-residential care and residential care. The services can be strongly intertwined with healthcare-related LTC services. Home care, first of all, assists in the activities of daily life (bathing, clothing, eating, shopping, cooking, etc.).

In Slovenia like in many other EU member states capacities of residential care in NHs do not satisfy the demand to provide room for all persons that applied for NHs. According to different sources of data, we can see that there were in Slovenia 17,783 NH residents older than 64 years at the end of 2016 according to data provided by National health insurance institute (ZZZS), 7,100 home care users at the end of 2015 according to information provided by Institute for social service provision of Republic of Slovenia as presented in the report of Nagode et al. (2014) and 6,417 applicants for NH according to Association of institutional care providers of Slovenia (SSZS). From data provided by Slovenian national health institute for 2016, we have calculated the probability that person in a cohort will be dependent on the help of others in a specified category of care.

Currently, we have available only yearly data regarding institutional care in the NHs, by age, gender and category of care from 1 to 3. We have added to this data the number of persons in the home care and number applications for institutional care (Table 4). We have calculated the probabilities that the older adult is dependent on the help of others in a specified category of care.

According to the study of Nagode et al. (2015a, 2015b), there were 866 assisted-living housing units in Slovenia in the year 2014 and according to to the research done by authors till 2017, the number has increased to 933. A number of the owner-occupied assisted-living housing unit is 335. According to data provided by SSZS, there were 20,602 beds in NHs in September 2017 in Slovenia. Currently, capacities in assisted-living facilities present less than 5% of capacities in NHs in Slovenia. The probability that an older person will be in a particular category of care in a NH and the probability that an older person will be dependent on the help of others and will need care in a specific category for male and female is presented in Table 5, while the category of care – probability matrix of the state of the system is given in Table 6 and the number of home care users from 1998 to 2015 in Table 7.

5.1 Actuarial model of long-term care insurance

We will use the following notation and abbreviations:

Pcx:h|LTC– yearly PR for LTC insurance for person x years old payable for h years (in the period of coverage, coverage starts at x years of age);

Pbx:h|LTC– yearly PR for LTC insurance for person x years old payable for h years (before the period of coverage, coverage for LTC claims starts at x + h years of age);

PxLTC– the single PR for LTC insurance for person x years old;a(x) = a_(x) – the present value of the lifetime annuity for €1, paid at the beginning of each yearfor the person that is x years old – according to the mortality table;

LTCa(x) – the actuarial present value of lifetime expenditures for LTC services for person x years old;

γ₂ – percentage of the administrative fee that insurance company charges at each payment of benefit;

γ₁ – percentage of the administrative fee that insurance company charges at each payment of PR;

_jp_x – the probability that person x years old will survive j years;

pxltc(cat)– the probability that person x years old is in the category of care [(cat)=I, II, III, IV].c_cat – yearly expenditure on LTC services in the category of cat=I, II, III, IV.

υ=11+i interest factor where I is an interest rate.

In the multi-state transition model with m categories of the intensity of LTC provision for older adults with declining functional capacities, there are possibilities of m + 1 transitions from one intensity of care to another. We denote the initial state (where the older adult is fully functional and does not need any care) as state 0 and transition, which require an intensity of care of type j by the line of the graph from this parent node to the child node j, j = 1, 2, …, m. On this graph, we should describe the probabilities of transition from the state 0 and further states to the child node (state) j ϵ CC or in general: from the parent node to the child node j at various ages. All paths to j determine the needed dynamics of development of community infrastructure for LTC provision with the number of serviced older adults in need of category of care of type j; it means the development of the required capacity of LTC provision of type j, which should be completed in a specific time τ. In the multiple decrement model, transitions between any two states from i to j, i > j = 1, 2, …, m, are not possible (directed graph) (57).

An older adult can move among various states regarding their functional capacities and needed care. Let us consider an older adult x denoted by (x). We denote the future period in which older adult will need the intensity of care in the category i ∈ CC by T_i(x). Thus, x + T_i(x) will be the age when the older adult because of declining in his functional capacities exits out of his or her current state i and enters a new state where he will have to receive the intensity of care in category j, j ∈ CC, which means a transit to a more intensive category of care of type j or he exists the system due to death. The future period in which older adult will need the intensity of care in the category i, T_i(x), is a random variable with probability distribution function:

The function G_i(t) represents the probability that the older adult will die or transfer to a more intensive category of care j (state j) within t years, for any fixed t. We assume that Gi(t), the probability distribution of Ti, is known. We also assume that G_i(t) is continuous and has probability density g_i(t) = G_i’(t). Data for Gⁱ(t) should be available from national statistics. Thus, one can describe:

Similarly, one can write:

Equation (4) denotes the probability that a worker aged x will remain in his or her current state at least t years.

The transitions are successive according to the decline in functional capacities and the available intensity of care in the needed category. Let us denote: i = 0: fully functional older adult not in need of any care.i = 1: the intensity of LTC is 0.5 h per day (LTC1);i = 2: the intensity of LTC is 1 h per day (LTC2);i = 3: the intensity of LTC is 1.5 h per day (LTC3); and i = 4: the intensity of LTC is such that can only be provided in the NH (LTC4);i = 5: functional capacities decrease to such a low level that older adults die (D).

Based on the data from the National Health Institute and Statistical Office, one can derive the expected needs of seniors at the national, regional or city/municipality level.

The probability q_x^(i,j) that the functional capacities of the older adult that are currently receiving care in the category i will decline in such extent that she/he will need the intensity of care in category j for person x years old is written by:

Where M_x^(i,j) is the number of older adults that transit from category i to category j and L_x⁽ⁱ⁾ is the total number of older adults who were previously were receiving care in category i-1. Here p_x⁽ⁱ⁾ is the probability that the person is staying in the same category of care i. In the year τ, the final structure of insured older adults by type of care needed for each person x-year-old in the cohort τ is described by the transition matrix (2). The basics of such transition are described in (58) and (59), only for the age – dependency structure:

After such a transition in the year τ – 1, the structure of adapted homes needed by local older inhabitants is L_x,τ:

The data should be available from the National Statistics Office. Currently, the data are not publicly available but are collected by the National Health Insurance Institute and not elaborated as needed for our planning the allocation of residents by type of facility in the year τ + 1 (when they are x + 1-year-old) is:

The structure of the population of older adults according to the total needed intensity of care can be written as:

Actuarial present value as the present value of probability-weighted cash flows of expenditures for LTC services for an older adult who x-year-old in year τ is dependent on the help of others is:

Insurance for covering expenditure for LTC services for a senior who is dependent on the help of others could be single or yearly PRs:

• The single PR for lifetime LTC for person x years old in year τ:

  (14) P τ x L T C = ( 1 + γ 2 ) ∗ L τ T C a ( x ) = ( 1 + γ 2 ) ∗ ∑ j = 0 100 − x p j τ + j x ∗ ϑ j ∗ ( p τ + j x + j L T C 1 ∗ c 1 + p τ + j x + j L T C 2 ∗ c 2 + τ + j p x + j L T C 3 ∗ c 3 )

• Yearly PR for LTC insurance for person x years old in the year τ, where the PR is payable h years (coverage starts after h years):

  (15) Pτx:hLTC=pjτx∗ϑj∗(1+γ2)∗LτTCa(x+h)(1−γ1)∗∑j=0n−1pjτ+jx∗ϑj=hτpxk∗ϑh*∗(1+γ2)∗∑j=0100−(x+h)τ+jjpx+h+∗ϑj∗(τ+jpx+h+jLTC1∗c1+τ+jpx+h+jLTC1∗c2+τ+jpx+h+jLTC1∗c3)(1−γ1)∗∑j=0h−1jτ+jpx∗ϑj

• The PR for LTC insurance for person x years old in the year τ, at the closing of LTC insurance contract where the PR is payable n years (coverage starts at age x):

  (16) P τ 65 : 16 L T C = ( 1 + γ 2 ) ∗ L τ T C a ( 65 ) ( 1 − γ 1 ) ∗ ϑ n − 1 ϑ − 1

Actuarial formulas for calculation of PRs for longevity insurance presented in this chapter are for single life. Equations for joint life in the case that insurance would cove longevity of couple who own the property is presented in Gerber (1980).

5.2 Numerical example of long-term care insurance for implementation in Slovenia

Let us suppose that person dependent on the help of others needs the intensity of care as presented in Table 7 with the yearly expenditure for LTC – the social care as given in Table 8:

We will calculate the PR for the male, which will cover expenditures of LTC in the category of required care for a person who is dependent on the help of others:

• Mortality tables used for calculating annuity PR are the same as are prescribed by the Slovenian Agency for Insurance Supervision for calculating mathematical reserves (DAV 1994 R)

• The technical interest rate is 1.75%, discount rate = 1/0.0175 is

• Administrative costs γ₁ that insurance company charges in the period of payment of PR are 5% of the PR

• Administrative costs γ₂ that insurance company charges in the period of payment of benefits are 5% of the benefit paid.

• The probability that older adult is dependent on the help of others in a particular category of care was calculated from:

• data on LTC insurance (number of users by age, sex and category of care) for the year 2016 provided by National Health Insurance Institute and

• data on waiting list for residential care provided by Slovenian Association of Institutional Care Providers from April 2016.

• The data on expenditures for the social part of home-care (for one hour of home care per day – €16) was provided by Social Protection Institute of Slovenia and is the same as the average in 2016.

• The intensity of care used in Categories of care is 0.5 h per day for the category I, 1 h per day for the category II and 1.5 h per day for the category III.

The PR P25:40|LTC for LTC annuity with the actuarial present value LTCa₆₅ in an LTC insurance scheme where contributions are paid for 40 years and benefits are paid from age 65 when a person becomes dependent on the help of others:

• The single PR for lifetime LTC for a person 65 years old:

  P65LTC=(1+γ2)∗LTCa(65)=(1+γ2)∗∑j=0100−65jp65∗ϑj∗(p65+jLTC1∗c1+p65+jLTC2∗c2+p65+jLTC3∗c3)=(1+0.05)∗∑j=0100−65jp65∗ϑj∗(p65+jLTC1∗2,880+p65+jLTC2∗5,760+p65+jLTC3∗8.640)=5,363.46∗1.05=5,631.64€

• Yearly PR for LTC insurance for a person 25 years old where the PR is payable 40 years:

  P25:40|LTC=40p25∗ϑ40∗(1+γ2)∗LTCa(65)(1−γ1)∗∑j=0n−1jpx∗ϑj=

       =p4025∗ϑ40∗(1+γ2)∗∑j=0100−65pj65∗ϑj∗(p65+jLTC1∗c1+p65+jLTC2∗c2+p65+jLTC3∗c3)(1−γ1)∗∑j=040−1pjx∗ϑj==p4025∗ϑ40∗(1+γ2)∗∑j=0100−65pj65∗ϑj∗(p65+jLTC1∗2,880+p65+jLTC2∗5,760+p65+jLTC3∗8.640)(1−γ1)∗∑j=040−1pjx∗ϑj=0.45001∗0.49960∗(1+0.05)∗5,363.46(1−0.05)∗28.37712=46.97€

• The PR for LTC insurance for a person 65 years old where the PR is payable for 16 years:

  P65:16LTC=(1+γ2)∗LTCa(65)(1−γ1)∗ϑn−1ϑ−1=420.64€

The numerical example is based on currently available data and the results are crude numbers due to lack of data. However, as in the numerical case the model is using observed patterns from the institutional care, which is reflecting not only demand (needs) but also supply, the probabilities of social care utilisation is expected to change because of change in behaviour of users of social care services and increase in procurement of services after introduction of reverse mortgage product.

5.3 Optimal transitions among facilities

An individual’s independence and autonomy do not depend exclusively on his or her physical and cognitive abilities but also on the environment. The rate of functional decline is mainly dependent on and linked to the way of life and external social, environmental and economic factors.

Knowing the possible and desired options of older inhabitants to move in a housing unit in an assisted living facility, we shall model the demographic structure of population distributed among different types of facilities, and therefore, demand for new and more accommodative facilities.

The migrations need to be monitored and reported based on the functional capacities of residents. Figure 2 shows the graph of movements among different types of facilities, which will be under consideration. The notation in the diagram is the following (see the details in Bogataj et al., 2016):

We denote the initial state as state 0 and the decrement, which requires facility of type j by the line of the graph from this parent node to the state (child node) j, j = 1, 2, …, m. On this graph, we describe the probabilities of transition from the state 0 to further states to the child node (state) j ϵ H or in general: from the parent node to the child node j at various ages. The probabilities depend on the age structure, functional capacities, preferences to move and the financial abilities and support networks of the potential users. All paths determine the needed dynamics for constructing the proper capacity of facilities of type j; it means inventories of different type of facilities in the process that should be completed at the time forecasted.

The transitions are successive according to the functional capacities, the available intensity of care and available facilities. We shall denote

i = 0: FH family home with fully functional and autonomous residents without the need for care;

i = 1: homecare in the adopted family home (adFH);

i = 2: housing unit in sheltered housing campus (SH);

i = 3: housing unit with available care services (HwC); and

i = 4: NH;

i = 5 dead (D).

We shall denote by i the type of housing unit in which the resident is currently residing (i = 0 to 4); and by j the type of housing unit to which the resident is moving due to declining functional capacity (resettlement from the type of facility i to j; j = 1 to 5). The details of the migrations can be modelled as a directed graph in Figure 1, as simplified in Figure 2. Based on the demographic statistics, including the population’s income, one can calculate the expected needs of older adults in the studied area and the probabilities of transitions among the different types of dwellings. Such transitions can be financed by personal insurance products, properly developed reverse mortgages schemes or based on national insurance schemes (Bogataj et al., 2015a, 2015b, 2016; Bogataj and Bogataj, 2015).

To successfully forecast the different accommodation needs of older adults – and therefore, the optimal structure of the facilities – based on the decreasing functional capacities of residents and the effective demand, we must know the probability distribution of ^FT_i(x), the time that an older adult will spend in the facility of type i, i ∈ H. We suppose that the resident moves to the type of facility that optimally suits his/her functional capacities. The probability of transition in the model should be calculated based on the results of surveying among the older adults and the observations of moving from one type of facility to another if the supply is high enough and the facilities are affordable.

The transitions are successive according to the functional capacities of residents, the available intensity of care and available facilities. We shall denote

:i = 0: FH family home with fully functional and autonomous residents without the need for care;

i = 1: homecare in the adFH;

i = 2: housing unit in SH;

i = 3: assisted living facility – HwC; and

i = 4: NH;

i = 5 dead (D).

The optimal structure of facilities is the structure, which accommodates residents’ functional capacities so that tenure in the community i, (i = 1, 2, 3) maximise ^FT_i(x) so that the relocation to the NH is postponed maximally.

5.4 Modelling flexible reverse mortgage

In the paper, we shall develop a reverse mortgage model with embedded longevity and LTC insurance for financing LTC expenditures and optimal housing arrangement for persons with declining functional capacities.

Reverse mortgage transforms the value of fixed assets in owner-occupied dwellings into liquid assets for covering LTC and housing-related costs for elderly homeowners. They, thus, enable a homeowner to access the wealth accumulated in the form of the home, while being able to continue to live in it. An illiquid asset becomes a source of liquidity, mainly for financing needs of persons that are dependent on the help of others. A reverse mortgage is a loan that will be repaid from the sale of a property, mainly after the death of the owner. Reverse mortgage is, therefore:

• financial service;

• source of liquidity for the future;

• contain a strong entitlement to remain in occupation of the property; and

• rely solely on the sale of the property for repayment/payment of the funds released to be used as a retirement pension.

The holder of a reverse mortgage contract can choose between different cash flows:

• lump-sum payment or;

• periodic (monthly, yearly) income; and

• cash on demand.

The loan is secured using a mortgage on the property. Reverse mortgage contract stipulates that repayment is made from the proceeds of the sale of the property either after the death of the homeowner or when the property has become vacated for a longer time (see details on European implementations in Reifner et al., 2009).

The actuarial notation used is described in Gerber (1980). For modelling Reverse Mortgage Contract, we use Lifetime annuity at the moment of closing of the reverse mortgage contract. The value of the property is used for repayment of the reverse mortgage loan.

Let us replace the standard notation used in actuarial mathematics as follows: a(x) = a_(x)The actuarial present value of the lifetime annuity for €1, paid at the beginning of each year for the person that is x years old – according to the mortality table; p(j|x) = _jp_xthe probability that the person that is x years old will survive the next j years:

ν = 1/(1+i)discounting factor where i is the annual interest rate

The amount of yearly disbursement of the lifetime annuity, therefore, needs to cover the interest on the principal amount taken out and the annuity paid to the beneficiary of the reverse mortgage:

The amount of lifetime annuity is calculated as the annuity factor multiplied by the net VRE, which is calculated as the VRE minus the cost associated with the transaction (valuation costs, taxes, costs of sale).

We shall further use the more simple expression as annuity factor fr(x, i), which is:

In equation (18) the rate γ₂ represents the costs associated with the disbursement of the annuity, that the insurance company charges for each pay-out, in the period of the annuity.

The yearly amount of annuity R_h is calculated according to the value of real estate VRE and annuity factor fr(x, i):

Here C are all costs associated with closing the reverse mortgage contract and with the sale of the property after the death of the beneficiary.

The maximum amount of loan (MLA) that can be drawn from the real estate is the VRE minus all the costs (C), i.e. those associated with closing the reverse mortgage contract (C₁) and with the sale of the property after the death of the beneficiary (C₂).

A life annuity consists of a series of payments, which are made while the beneficiary (of initial age x) lives.

The present value of the life annuity due with yearly payments at the beginning of each year for €1 in next n years for a person, which is x years old, is denoted by a(x|n), where the following equation can be written:

The present value of the life annuity deferred for n years with yearly €1 payments is denoted by b(x,n) = _n|a_(x), where the following equation can be written:

The PR rate for longevity insurance prs(x, i, n) is:

Where γ₁ represents the rate of administrative expenses that are charged against the policy in the period of PR payments and γ₂ represents the rate of administrative costs that are charged against the policy in the period of annuity payments. The yearly amount of PR is calculated as:

Where R_h is the annuity amount withdrawn from the housing asset. In this case, the yearly disbursement amount that the beneficiary can draw from the real estate is:

When functional capacities of homeowner decline to such level that he is no longer able to live in his own house, the homeowner’s housing equity is used to purchase supported housing unit in the assisted-living facility or retirement community of homeowner’s choice.

5.5 Numerical example of housing equity withdrawal scheme in Slovenia

We shall study the dynamics of the reverse mortgage income, calculated based on 1.75% interest rate on the outstanding loan and 1.75% discount rate embedded in the deferred lifetime annuity PR (male population, DAV1994R) and mortality tables for payment of PRs for male population after 65 age (male population, Slovenian mortality Tables 2007) at the following other parameters, as considered in Table 9:

• Age of residential property owner at the closing of the reverse mortgage contract is 65;

• Value of the property is constant at €160,000;

• The discount rate used by the insurance company for the calculated annuity PR is 1.75;

• Mortality tables used for calculating annuity PR are the same as are prescribed by the Slovenian Agency for Insurance Supervision for calculating mathematical reserves (DAV 1994 R);

• Administrative costs for payment processing and disbursement are estimated at 5% of the PR and annuity amount accordingly;

• The interest rate on an outstanding loan charged by the financial institution is 1.75%;

• Closing costs are counted at 2% of the value of the property;

• Accounting costs are fixed at €120 per amount;

• Longevity PR amounts €2,948.98;

• LTC PR is calculated as NPV of LTC costs for social care based on the healthcare tables (ZZZS, 2017): €8 per 0.5 h, €16 per 1 h, €24 per 1.5 h per day, the yearly PR payable for 16 years: €420.64; and

• Monthly disbursement for €333.33.

In the case of the residential property value, which equals €160,000, which is not growing through the time horizon of owners lifespan all the costs associated with the closing of a reverse mortgage contract (brokerage fee, assessment fee, notary fee and other administration costs) are 2% (€3,200). The yearly amount drawn from the residential real estate equity is equal to €7,517.18. This amount is then divided into three parts €120.00 covers administration fee, for maintaining reverse mortgage account with a financial institution, the amount of €2,948.98 is used for purchasing the annuity PR that covers the annuities after exhausting all the equity in the residential real estate property (in case that real-estate owner is living longer than expected). The yearly amount of €4,000 is disbursed to the property owner, who is staying in his property until the end of his life in any case. At the end of his life, the costs of refurbishing and selling the property are covered by remaining €7,156.46. After renovating the house is sold for €160,000, which was also estimated price at the beginning of the time horizon of our simulation.

5.6 The transition from own home to a privately owned assisted-living housing unit

Let’s assume the case that after living in his owned house of 11 years function capacity of homeowner declines so that he is no longer able to live in his own home under the stipulation of flexible reverse mortgage contract he is allowed to sell his hose unit and buy assisted-living housing unit for €120,000. The proceeds of sale above the purchase price for €40.000 are used for repayment of the loan and the new reverse mortgage scheme is the following, as given in Table 10:

5.7 Mitigating the risk of dependence on the help of others

To prevent adverse selection and moral hazard assessment of LTC risk should be part of the underwriting process. Right to coverage of the social part of home-care and community care services under the LTC insurance contract should be subject to the individual’s risk assessment. Eligibility and risk PR should be based on the professional assessment of functional capacities of the beneficiary, physical characteristics of the housing unit and social care needs of insured. The proper prescription process should be defined. Without adequate insurance for LTC risks, real estate cannot be used as the vehicle for financing LTC expenditures in community care, because the equity release without LTC insurance presents a considerable risk for the insured older adult that he will not have sufficient funds to cover LTC expenditures when he becomes dependent on the help of others. The standard annuity does not cover increasing expenses for care due to declining functional capacities of the beneficiary.

Housing equity scheme, including LTC insurance, can be underwritten even when the need for care has already materialised. However, then the risks and associated probabilities are different. Reverse mortgage contract, which is underwritten, when the homeowner is already dependent on the help of others, has different probabilities τ+jpx+jLTC1, τ+jpx+jLTC2, τ+jpx+jLTC3 that insured will be dependent on the help of others and in a particular category of care. The actuarial present value of LTC services provided should be calculated under the assumption of the equivalence of the actuarial present values.

5.8 Mitigating the risk of longevity

The main risks concerning the reverse mortgage that can cause credit default are:

• the uncertain longevity of the owner-occupier, realised when the value of a property being sold does not cover the amount of loan;

• the risk of an increase in interest rates;

• and depreciation in the value of the property, subject of some political reasons (Černe et al., 2012).

Deferred annuity as insurance for longevity is already used in the insurance industry, but not in combination with a reverse mortgage as the one proposed here. Sustainability and market consistency regarding longevity are among the main concerns of The Actuarial Association of Europe¹.

Without adequate insurance for longevity and LTC risks, real estate cannot be used as the vehicle for financing LTC expenditures in community care, because the equity release without longevity insurance presents a considerable risk for the provider of a reverse mortgage (bank) and is not covering increasing expenditures for the care of the beneficiary. For the reverse mortgage provider, there is the risk that the value of the loan together with accrued interest will be higher than the VRE in case of the death of the beneficiary. For the beneficiary, there is the risk that he will live longer than the agreed period of drawing liquid amounts that are defined in the reverse mortgage loan contract. A safe reverse mortgage contract also needs to include a kind of insurance for longevity. This insurance can be provided in three ways:

• Through public finance so that the risk is socialised and the management of risk is assumed by the government (as is the case in the USA where The Home Equity Conversion Mortgages Insurance is a clear example of such a scheme. Lenders under this programme are protected against losses arising when the loan balance exceeds the VRE at the time of settlement. However, because of implicit government guarantees underlying this insurance, it may become a severe drain on the fiscus, as the market expands after the crisis, as also described by Wang et al. (2008) and Chen et al. (2010);

• The risk can be transferred to insurance companies. According to the results in Blake et al. (2013), the enormous economic significance of the longevity risk has begun to be recognised and quantified in their article, presenting the birth and development of the Life Market, the new market related to the transfer of longevity and mortality risks. The authors note that the emergence of a traded market in longevity-linked capital market instruments could act as a catalyst to help facilitate the development of annuity markets, both in the developed and the developing worlds and protect the long-term viability of retirement income provision globally. The possible instruments have been studied and developed also in Lee et al. (2012) and Yang and Wang (2013);

• The third way is possible through a mutual insurance company, as proposed in Bogataj (2013a, 2013b) and inherently present in this paper. The risk of longevity can be mitigated by the use of annuity insurance where legal, obligatory mortality tables in Slovenia are German DAV1994R, which is close to mortality projection 2050; hence, insurance companies benefit on an overestimation of longevity today. Indeed, it is better to share the benefit of this overestimation among the remaining seniors, but it is difficult to avoid the impact of the volatile interest rate (Figure 3).

As followed from Figure 1, in the past 67 years, the long-term interest rate was very volatile and it was in the range between 2 and 16. Long-term interest rate influences the affordability of reverse mortgage for homeowners.

We can calculate PRs for LTC insurance at a different interest rate, as presented in Table 11.

From Figure 4, we can see that real estate values fluctuate over time, so in the event of a collapse in the value of real estate market, there is a risk that the bank, as a lender, will not be able to settle the reverse mortgage loan by selling a property.

But nominal values were growing for most of the time (Figure 5)

Table 12, Showing the relative frequency of indexes of nominal real estate price growth over 22 years – moving 22-year intervals, explain that in the USA, in the time horizon 1890–2012 only in 3% of 22 years moving ranges the price after 22 years was lower than at the beginning of the interval. The highest drop in the nominal values was equal to 16%. This risk we can mitigate by futures and future options on Case-Shiller index, traded on the Chicago mercantile exchange